# Syllabus 2017

IMPORTANT

Our syllabus can be seen at the website of KULASIS since 2019.

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## Course Title : Engineering Mathematics B1

Code | 20510 |
---|---|

Course Year | 2nd year |

Term | |

Class day & Period | T1.T2：Wednesday・5,T3.T4：Friday・3, |

Location | kyotsu155 |

Credits | 2 |

Restriction | No Restriction |

Lecture Form(s) | Lecture |

Language | Japanese |

Instructor | T1.T2:E. Harada,T3.T4:J. Saitoh, |

### Course Description

The course introduces theory of complex functions and its applications.

### Grading

Term-end examination and attendance.

### Course Goals

To understand the properties of regular function. To learn Taylor expansion and Laurent expansion. To calculate residues. To learn some applications for engineering.

### Course Topics

Theme | Class number of times | Description |
---|---|---|

Introduction | 2 | Definition of complex numbers, complex plane and review of vector analysis |

Basic theory of complex functions | 8 | Derivative of complex functions. Cauchy-Riemann equations. Concept and properties of regular functions. Cauchy's integral theorem. Cauchy's integral formula. Taylor series and Laurent series. Classification of singularities. Residue theorem. Various complex functions and their properties. |

Application of theory of complex functions | 4 | Application of residue theorem to calculation of definite integrals. Multivalued functions. |

Learning achievement test | 1 | Learning achievement test. |

### Textbook

None.

### Textbook(supplemental)

Useful material is introduded during the lecture.

### Prerequisite(s)

Basic Calculus (From the university curriculum: Calculus A and B, Advanced Calculus A).